Question

option #5
your first option is to build the roof that has the measure of the two combining top angles of 120°.
what is the value of x?
x =

Explanation:

Step1: Set up the equation

Given \(m\angle AEB + m\angle DEB=120^{\circ}\), and \(m\angle AEB = 2x^{\circ}\), \(m\angle DEB=(5x - 6)^{\circ}\).
So, \(2x+(5x - 6)=120\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+5x-6 = 120\), which gives \(7x-6 = 120\).

Step3: Isolate the term with \(x\)

Add \(6\) to both sides: \(7x-6 + 6=120 + 6\), so \(7x=126\).

Step4: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{126}{7}\).

Answer:

\(x = 18\)